Visual Computing

University of Konstanz
Geometry Processing

GPU-assisted Positive Mean Value Coordinates for Mesh Deformations

Y. Lipman, J. Kopf, D. Cohen-Or, D. Levin
Teaser of GPU-assisted Positive Mean Value Coordinates for Mesh Deformations

Material

Paper (.pdf, 7.1MB)

Abstract

In this paper we introduce positive mean value coordinates (PMVC) for mesh deformation. Following the observations of Joshi et al. [JMD*07] we show the advantage of having positive coordinates. The control points of the deformation are the vertices of a "cage" enclosing the deformed mesh. To define positive mean value coordinates for a given vertex, the visible portion of the cage is integrated over a sphere. Unlike MVC [JSW05], PMVC are computed numerically. We show how the PMVC integral can be efficiently computed with graphics hardware. While the properties of PMVC are similar to those of Harmonic coordinates [JMD*07], the setup time of the PMVC is only of a few seconds for typical meshes with 30K vertices. This speed-up renders the new coordinates practical and easy to use.

BibTeX

@inproceedings{Lipman2007GPUassistedPositive,
  author    = {Y. Lipman, J. Kopf, D. Cohen-Or, D. Levin},
  booktitle = {Geometry Processing},
  doi       = {10.2312/SGP/SGP07/117-123},
  editor    = {Alexander Belyaev and Michael Garland},
  isbn      = {978-3-905673-46-3},
  issn      = {1727-8384},
  publisher = {The Eurographics Association},
  title     = {GPU-assisted Positive Mean Value Coordinates for Mesh Deformations},
  url       = {http://www.math.tau.ac.il/%7Elipmanya/pmvc/pmvc.htm},
  year      = {2007}
}